Find the sample standard deviation and the population standard deviation of the data set. 70, 58, 70, 37, 58, 47, 58, 76, 77, 67, 66, 77, 33, 74, 57

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From the Data set given, we will solve for population standard deviation using the formula. standard deviation = 1/n[[latex] \sqrt({x} -mean)^{2}[/latex] mean = sum of all data/number of data mean =925/15 mean=61.67 x


The formula for the sample standard deviation (denoted as s) and the population standard deviation (denoted as the greek letter sigma ∅) is shown in the picture where, x is each entry of data overbar x or ∪ is the mean or average n or N is the number of data which is 15 They are just basically the same except for the denominator. First, let's determine the mean overbar x or ∪ = (70+58+70+37+58+47+58+76+77+67+66+77+33+74+57)/15 = 61.7 The numerator would be [(70-61.7)^2+(58-61.7)^2+(70-61.7)^2+(37-61.7)^2+(58-61.7)^2+....] and so on and so forth. The denominator for the sample is n-1 = 14, while the denominator for the population is n=15. Substituting the formula: s=13.94 ∅=13.47

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